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I've been studying Capacitance and Dielectrics and I can't understand why the capacitor will only discharge if there is a wire connecting them. I understand that when the capacitor is charged up, there is an electric potential difference between the plates that makes the electrons "want to move" from the higher to the lower potential. But since the plates have opposite charges and charges are at the surface of the conductors, why can't the charges move from the positive plate to the negative plate due to Coulomb force?

Apologize me if this is a basic question, but I've been looking for this answer and I just can't find anything of the like, must be because it is really basic.

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  • $\begingroup$ Ideally, there is no path for the charges to return. Imagine two plates separated by vacuum. How will the charges get from one to the other? In reality, there are paths: surface states, impurities, moisture, grease, etc. So ideal capacitors do not discharge, but real ones always do, eventually. $\endgroup$
    – garyp
    Commented Oct 24, 2016 at 19:28
  • $\begingroup$ But why won't the charges go from the positive plate to the negative plate attending to the fact that the electric field lines point from the positive to the negative charge? $\endgroup$
    – George Sailor
    Commented Oct 24, 2016 at 19:31
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    $\begingroup$ The electrons are also attracted to the positively charged nuclei in the plates, so it takes a huge electric field to rip them off. For high enough fields, it can happen; this is called "electric breakdown". $\endgroup$
    – knzhou
    Commented Oct 24, 2016 at 19:48
  • $\begingroup$ Well but in that case it will also be difficult to rip them off through the wire no? The positive attraction is still there. Besides, in conductors it is said that the electrons are poorly attached to the nuclei $\endgroup$
    – George Sailor
    Commented Oct 24, 2016 at 20:04
  • $\begingroup$ @GeorgeSailor No, because if electrons go through the wire, they never have to leave the metal. $\endgroup$
    – knzhou
    Commented Oct 24, 2016 at 20:35

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The Coulomb force is a force trying to move electrons from one plate to the other. That is correct. But remember that there are more forces working here.

There is a huge resistance against charge motion in an insulator. The resistance pushes back and prevents electrons from just moving into thin air.

In other and more accurate words: that resistance prevents electrons in the air molecules from moving freely. Only then would air be conducting. Electrons move freely in a metal for example but are bound much tighter in an insulator. So it is not possible to make the "chain reaction" of electron motion happen; it is not possible for an electron on the plate to pass on its "motion" to the neighbor electron in the air molecule, which would then pass it on and on and on all the way to the other side.

If you wish to make the electrons in the insulating air move (become excited) despite the resistance, you either have to

  • add enough energy to the air in between for example by making the potential difference so enormously high that electrons can rip themselves loose from the air molecules and move freely (ionizing the air), which is what lightning is all about, or

  • connect an easier path between the plates. For example by a metal wire, through which this "chain reaction" of electron motion can happen easily.

What you are asking is pretty much the basic reason for conductivity in some materials and insulation in others. This is all about the band gap, which electrons have to jump over in order to be free to conduct. And by jumping over, I mean that they have to jump to a higher energy level - they don't physically jump, they just rip themselves loose at the spot they are at. There is no band gap in conductors, but a large one in insulators. And a smaller one in the so-called semiconductors. The above explanation is a try to make that a bit intuitive. I hope it helps you on.

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Think about it using Ohms Law. You got a layer of air (or any dielectric) between the plates. It happens that the difference of potential is not big enough to make the electrons move in the air (the air is not a very good conductor). Some capacitors have dielectrics because their operation happens in bigger potential differences (the dielectric will be a even worst conductor than the air).

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  • $\begingroup$ I understand what you mean. But when there are two isolated charges in space, they will attract or repel each other, and move independently of the matter inbetween. Why is it different now? $\endgroup$
    – George Sailor
    Commented Oct 24, 2016 at 19:34
  • $\begingroup$ @GeorgeSailor First: these charges are "free", not in an atom (also, in an electric current the electrons dont actually "move" all the distance around, i recommend you to read about it, the electrons move in a velocity around $10^{-3} m/s $ ) and second: when you study these kinds of problems in electrostatics, its almost always in vacuum. $\endgroup$
    – embedded_dev
    Commented Oct 24, 2016 at 19:51
  • $\begingroup$ Alright I think I understand it. But why does the wire make a difference to this then? $\endgroup$
    – George Sailor
    Commented Oct 24, 2016 at 20:06
  • $\begingroup$ The wire is a good conductor. $\endgroup$
    – embedded_dev
    Commented Oct 25, 2016 at 12:31
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The Coulomb force is there but in the ideal situation the air and the dielectric contain no free /mobile charge carries, that are insulators, so there is no mechanism for a current to flow between the two metal plates.
In the real world because the air and the dielectric are not perfect insulator the capacitor will discharge.

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